Problems with estimating the growth of a population.

#1
Hello to all, and many thanks for reading. I'm currently faced with a problem that, quite frankly, is driving me insane.

I'm trying to calculate an estimate, for each decade between 1800 and 2019, of the number of German-descent population in North America (Canada and the U.S.). I came up with something of a methodology to do that, based on some facts from 1790: that Germans made up 8,7% of the white population of the United States, that the white population of the U.S. numbered 3,172,006, and that the total population of North America was (approximately) 5,644,983. A detailed explanation is in the attached document, as well as the table with the results of those calculations.

The problem is that this produced impossible numbers of Germans (over a hundred million today, when the U.S. Census of 2010 barely registers more than forty million). I can see by now that this is because I'm assuming that Germans grow and keep growing at the same rate that the overall population, but still think that there must be some way in which I can accurately estimate their historical numbers. Can you help me, oh mighty statistical wizards?
 

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noetsi

Fortran must die
#3
Doesn't the census tell you the actual percent, I don't know why you have to calculate anything?

One issue is that you have a structural break in roughly 1920. At that point US immigration law changed dramatically. So percent change should be started from scratch with the 1920 base and a new growth from there.